5 Answers
5

In order to forbid trimming the hair of the mustache you would have to assume that it is forbidden due to the prohibition of lo tilbash (loosely: men can't perform "women's" actions and vice versa) and that lo tilbash still applies to shaving despite the fact that the majority of men in the world shave their faces entirely. Alternatively you can hold like the Tzemach Tzedek (YD 182) that all facial trimming is forbidden, at least miderabanan. (I think this opinion still requires the mustache to be considered one of the 5 corners. See next paragraph.) Both of these opinions appear to be minority ones (in my opinion). Also important is to note the Shulchan Aruch YD 390:1 which in discussing the laws of mourning, permits someone during sheloshim to trim his mustache if it is obstructing his eating. Clearly not all mustache trimming is forbidden.

In order to forbid shaving the hair of the mustache you have to assume that the implement you are using to cut with is forbidden to use to shave with (certainly a razor blade; possibly an electric shaver). Also you have to assume that the mustache is one of the 5 corners of the beard that we are forbidden to destroy. The Tur in YD 181 lists two different opinions about what these 5 places are. One opinion, Rabbeinu Channanel's, includes the two "corners of the mustache." The Tur also quotes the Rambam that the entire mustache is not included in the prohibition. It thus seems likely that at least the center of the mustache is not considered a corner.

However, it is important to note the words of the Rosh which are quoted in Shulchan Aruch YD 181:11 that since there are so many opinions about where exactly the corners are, we do not shave anywhere on the beard with an implement that destroys the hair in a forbidden way. I think those words are the strong tradition among Jews and are applicable here as well.

Thus there is certainly room to forbid shaving the mustache with a razor blade (and possibly an electric shaver).

I cannot comment regarding kabbalistic concerns.

[I used the definitions of trimming and shaving brought in the question.]

+1 for the Rabbeinu Channanel and the Rambam. I'll edit my question to make it clearer. I refer davka to those poskim who forbid cutting one's beard even not with a razor (electric shaver, scissors).
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HodofHodJan 5 '12 at 21:54

@HodofHod You're more than welcome to ask a separate question about the Halachik status of electric shavers.
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Double AA♦Jan 5 '12 at 21:59

ok thanks for the clarification. I'm not going to ask the electric shaver question, I'm already familiar with arguments for and against. I'll leave it for someone else. :)
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HodofHodJan 5 '12 at 23:01

Accepting this answer as it's the only one that brings any reason why it might be asur.
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HodofHodFeb 13 '12 at 4:24

The Lubavitcher Rebbe writes that he didn't hear any explicit instructions with regards to trimming a mustache (in the footnote it mentions that the discussion is only when the mustache impedes ones eating, though I don't know the source of this footnote). Moreover, there are logical reasons to forbid as well as to permit. Therefore, he suggests asking Rabbonim who knew what older Chassidum used to do.

The footnote is just explaining the question that the Rebbe was answering.
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MenachemJan 5 '12 at 22:37

...and it is printed together with the letter itself in Igrot Kodesh.
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MenachemJan 10 '12 at 20:38

FWIW, I asked R' Itche Meir, he said that some of the elter chassidim did (I think he mentioned R' Peretz). He doesn't, though. He says that if you cut it, it'll keep growing and you'll have to keep cutting it. If you just brush it to the sides, it stops growing eventually.
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HodofHodFeb 23 '12 at 13:15

@HodofHod - apparently the idea that cutting hair makes it grow more is an old myth. You can Google it if you like.
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DaveFeb 24 '12 at 0:32

@Dave Interesting, I did not know that. I don't think that's what he meant though. I think he just meant that it may be more convenient to simply brush it out of the way rather than having to cut it every so often.
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HodofHodFeb 24 '12 at 0:39

Thank you for this information, but it doesn't really give any reason to forbid cutting the mustache, as both the previous version of this question and the current one ask for.
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HodofHodFeb 23 '12 at 21:43

One of the many reasons to not shave or trim a beard, is because Chesed of Hashem grows through the hair on the face, and by cutting your beard you may affect your 'reception' of Hashem's Chesed.

The question then is if the mustache counts as part of the beard. Arguments exist for and against the mustache being part of the beard. Those kabbalists who say that the mustache is from the face (as apposed to the lip) and that it is part of the beard (as opposed to some other thing) would hold that you can not trim it.

However, since there is a verse which says that the lips are red, so it can be learned that the mustache does not cover the lips. This would be a reason to allow the trimming of the mustache. Those who disagree learn it to just mean that the most holy and righteous would naturally not have their mustache grow over the lips. This then becomes a lesson on the dangers of inappropriate chesed.

Shaving only the mustache but keeping the beard may make a person appear to be Amish, which might be chukat akum (Vayikra 18:3, Rambam (Sefer HaMitzvot Lav no. 30), Sefer HaChinuch (n. 262)). All the moreso because the Amish do so for religious reasons.

Thanks for the answer! Funnily, I've been mistaken for Amish far too often, even with a mustache. Additonally, Chukas Akum seems to apply mostly to things that are immodest or (might) have idolatrous origins (see here), neither of which would seem to apply to the Amish mustache-ban (which seems to be anti-military in nature). If you have a specific source for this, or a reason to believe that Chukas Akum might apply to beards minus mustaches (as opposed to, say, beards plus overalls), I think it'd greatly improve this answer.
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HodofHodDec 16 '14 at 22:01

As I note, the Amish practice to not wear mustaches has its origins in their religion on some level. Whether that is close enough to idolatry or not is a great question.
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Ze'ev FelsenDec 17 '14 at 2:53